## Involve: A Journal of Mathematics

• Involve
• Volume 2, Number 2 (2009), 225-236.

### Congruences for Han's generating function

#### Abstract

For an integer $t≥1$ and a partition $λ$, we let $ℋt(λ)$ be the multiset of hook lengths of $λ$ which are divisible by $t$. Then, define $ateven(n)$ and $atodd(n)$ to be the number of partitions of $n$ such that $|ℋt(λ)|$ is even or odd, respectively. In a recent paper, Han generalized the Nekrasov–Okounkov formula to obtain a generating function for $at(n)=ateven(n)−atodd(n)$. We use this generating function to prove congruences for the coefficients $at(n)$.

#### Article information

Source
Involve, Volume 2, Number 2 (2009), 225-236.

Dates
Accepted: 17 January 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513799142

Digital Object Identifier
doi:10.2140/involve.2009.2.225

Mathematical Reviews number (MathSciNet)
MR2501339

Zentralblatt MATH identifier
1167.05007

#### Citation

Collins, Dan; Wolfe, Sally. Congruences for Han's generating function. Involve 2 (2009), no. 2, 225--236. doi:10.2140/involve.2009.2.225. https://projecteuclid.org/euclid.involve/1513799142

#### References

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